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The trace map on elliptic curve is surjective.

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#algebraic-number-theory #arithmetic-geometry
60
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Definition of Tate-Shafarevich group , direct product and direct sum

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#number-theory #algebraic-number-theory #elliptic-curves #arithmetic-geometry
135
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Completion of Mordell-Weil group $E(K)$?

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#number-theory #algebraic-number-theory #elliptic-curves #arithmetic-geometry #formal-completions
101
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Is it possible to construct geometrically the ($\phi$, $\Gamma$)-module corresponding to a $p$-adic representation coming from geometry?

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#arithmetic-geometry #hodge-theory #etale-cohomology #galois-representations
56
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Reduction of elliptic curve and trace map, $E_1(L)/\text{trace}(E_1(K))\to E(K)/\text{trace}(E(L))\to \tilde{E}(l)/d\tilde{E}(l)\to 0$?

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#number-theory #algebraic-number-theory #elliptic-curves #arithmetic-geometry
141
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Is the order of cokernel of trace map of elliptic curve a power of 2?

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#number-theory #galois-theory #algebraic-number-theory #elliptic-curves #arithmetic-geometry
116
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Genus $1$ curve over $\Bbb{F}_q$ always has rational points, exercise $10.6$ in Silverman

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#number-theory #algebraic-number-theory #curves #elliptic-curves #arithmetic-geometry
111
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Does Galois group acts trivially on kernel of reduction?

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#number-theory #algebraic-geometry #elliptic-curves #arithmetic-geometry
114
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Is there a known diophantine equation that describes the complement of the sums of 2 squares?

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#number-theory #algebraic-number-theory #diophantine-equations #arithmetic-geometry
104
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Group cohomology $H^1(G,M)$ , where $G$ is finite and $M$ is finitely generated

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#algebraic-number-theory #elliptic-curves #group-cohomology #arithmetic-geometry #galois-cohomology
95
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Can we make the rank of twist of a given elliptic curve over number field $0$ by infinitely many ways?

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#number-theory #elliptic-curves #arithmetic-geometry
63
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A question on an elliptic curve having endomorphism ring Z[i]

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#algebraic-geometry #elliptic-curves #arithmetic-geometry
117
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Rank of elliptic curves and number prime factors of discriminant

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#number-theory #algebraic-geometry #algebraic-number-theory #elliptic-curves #arithmetic-geometry
59
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Rank of elliptic curves does not decrease under field extension?

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#number-theory #elliptic-curves #algebraic-curves #arithmetic-geometry
51
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What is the natural map $E_D(\Bbb{Q})\times E(\Bbb{Q})\to E(\Bbb{Q}(\sqrt{D}))$?

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#number-theory #algebraic-geometry #algebraic-number-theory #elliptic-curves #arithmetic-geometry

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